At each training step, the model is given a noisy image crop \(x_t\) .
However, in contrast to DDPM [1]}, whose model predicts the added noise (as in origddpmloss), our model predicts the clean image crop \(\tilde{x}_{0,\theta }\) . The loss in our single-image DDPM is:
\(L(\theta ) = \mathbb {E}_{\mathbf {x}_0, \epsilon }\left[\left\Vert x_0 - \tilde{x}_{0,\theta }\left(x_t, t\right)\right\Vert ^2\right]\) 
